Schoenberg is dead

The work of art is primarily genesis

wrote Paul Klee, for whom art was a metaphor for creation. He conceived the work as "formation of form," not as a result. Similarly, Boulez would speak of the work as "each time generating its own hierarchy."

Boulez tends precisely to liberate the possibilities of a functional generation when he identifies the series as its nucleus: "Primarily chosen predecessor: Webern; The essential object of his investigations: the organization of the sound material.

He doesn't seem to forget, but he doesn't explicitly recall, that it was Webern himself who spoke of a music that "gives one the sensation of no longer being faced with the work of man, but of nature."

Note: Webern, not Schoenberg. Only a year after his death, in fact, Boulez would definitively bury Schoenberg, denouncing every aspect of his aesthetic as backward, contradictory, and contrary to the new organization of the sound world he himself had conceived:

Schoenberg's pen, in fact, abounds - not without provoking irritation - with fearsomely stereotypical writing clichés, representative, here too, of the most ostentatious and most obsolete romanticism.

This is the famous article, which appeared in the magazine "The Score" in 1952, full of the naive dogmatism that only a 27-year-old can exhibit, ending with the statement in capital letters: SCHOENBERG IS DEAD. [Here in Italy it was published in Note di Apprendistato, Einaudi, 1968]. It is the final act of condemnation of Schoenberg's inability to fully adapt his compositional language to the novelty of the twelve-tone method and the indication of Webern as the example to follow.

Pierre Boulez – Structures for Two Pianos Book I (1952)

To demonstrate what he declared in capital letters above, Boulez wrote the first book of Structures for Two Pianos, which constitutes, in practice, a manifesto for the extension of the serial principle to all parameters in a structuralism as refined as it is totalitarian.

We will now show some analytical traces of the first section (Structure I/a), based on the historic article that György Ligeti published in the journal "Die Reihe" (trans.: The Series) in 1958.

Everything in this work is predetermined. The entire composition is derived entirely from a single original formula: a series that, in homage to Messiaen, is taken from the first line of the Mode de valeurs.

NB: To enlarge the images, click on them.

The ritual transformations (inversion, retrograde, and inversion of the retrograde) are applied to the series, and to each of them, the 11 transpositions, thus obtaining the classic 48 series.
Starting from the transpositions of the original series (O) and its inversion (I), Boulez then generates two numerical tables obtained by replacing the notes with the numbers they have in the original series (this is what Boulez calls "encoding" the series).

These two matrices, read in both direct and retrograde motion, are then used to determine the durations, dynamics, attack modes, and the order in which the 48 series of pitches and durations are introduced throughout the composition, as follows:

Pitches
All 48 canonical series appear in the piece, but, mind you, only once each, equally divided between the two pianos (24 each).

Durations
Four duration tables are constructed, each consisting of 12 series (48 series in total, like the pitches), using the following method: in the above matrices, each number represents a duration, obtained by multiplying it by a base unit equal to a sixteenth note. Thus,
1 = 1 sixteenth note,
2 = 2 sixteenth notes = 1 sixteenth note,
12 = 12 sixteenth notes = dotted quarter note.
The 12 durations (from 1 sixteenth note to 12 sixteenth notes), therefore, are:

Consequently, the shortest duration in section 1/a is the 33rd note and the longest is the dotted quarter note.

Dynamics
Boulez constructs a correspondence between numbers and dynamics according to this scheme.

Unlike the durations, however, here we do not create 48 series, but only 2 using the diagonals of the two tables already seen.

Table 'O' is used by Piano I, and 'I' is used by Piano II. For example, the Piano I series is as follows:

12	7	7	11	11	5	5	11	11	7	7	12
ffff	mf	mf	fff	fff	quasi p	quasi p	fff	fff	mf	mf	ffff
2	3	1	6	9	7	7	9	6	1	3	2
ppp	pp	pppp	mp	f	mf	mf	f	mp	pppp	pp	ppp

These are 24 dynamics, the same number as the series used by each piano. Consequently, each of the 24 series will be played with one of these dynamics in its entirety.
Note that some dynamics are repeated in this series. Also note that not all are present (e.g., 4, 8, and 10 do not appear in Series O). This is a result of organizational choices that will give rise to various criticisms.

Attack Modes
There are 10 attack modes (the numbers range from 1 to 12, but there are some gaps)

Similarly to the durations, the series of attack modes is determined by the other diagonals of the tables.

Here too, the "O" is assigned to Piano I and the "I" to Piano II, and here too we have a series of 24, so each attack mode is used for an entire series. There are only 10 thanks to the fact that, as with the dynamics, the series derived from the diagonals do not contain all 12 values.

Pitch Series Order
The two matrices are also used to determine the order in which the series are used. Structure 1/a is divided into two main sections, each of which uses 12 series for each piano, as follows.

Piano	Series in Section A	Series in Section B
1	All O series in order I1	All RI series in order RI1
2	All I series in the order O1	All series of R in the order R1

Order of duration series
As for pitches, as follows

Piano	Series in Section A	Series in Section B
1	All RI series in RI order1	All I series in R order1
2	All R series in the order R1	All series of O in the order RI1

Global Form

As already seen, each piano plays 12 of the 24 series in each of the two sections. Since each series of pitches is also accompanied by a series of durations that includes all 12 values, each series also has the same metric duration, that is, 1+2+3+…+12 = 78 thirty-second notes. The piece, therefore, can be viewed as a set of subsections, each of which lasts as long as a series.
This, however, does not mean that each of the two sections lasts 12 times the series because, since the piano is polyphonic, it is also possible to play multiple series simultaneously. Furthermore, in at least two places, each piano plays a series as a soloist.
The two sections, therefore, are divided into subsections in each of which each piano simultaneously plays from 0 (tacet) to 3 series (voices), according to the following table.

	Section A	Section B

Subsection	1	2a	2b	2c	3	4a	4b	5	6	7	8	9	10	11
Piano 1 Series	1	2	2	0	3	1	2	1	3	1	2	2	1	3
Piano 2 Series	1	2	1	1	3	1	3	0	2	2	2	2	1	3
Total	2	4	3	1	6	2	5	1	5	3	4	4	2	6

	Total 24	Total 24

The density of the piece therefore varies as shown in the "Total" line, in a non-serial or symmetrical way.

Metronome

The metronome markings for the various sections are "lento," "molto moderato," or "moderato, quasi vivo." If, for short, we indicate them with L, M, and V and write the tempos of Structure 1/a, we note the following symmetry (which, however, has nothing to do with the serial principle):

M:V:L:V:M

Octaves
The distribution of notes across octaves is generally arbitrary. Only two principles can be deduced:

the range and wide intervals typical of serialism;
when the same note occurs in two or more overlapping series, it is played in unison.

Rests

The use of rests is restricted to cases where notes are played staccato. In these cases, their duration is sometimes shortened and the remainder is filled with rests. In general, however, rests are used only to clarify the writing.
It seems that Boulez deliberately wanted to avoid interrupting the exposition of the series by inserting unjustified rests.

Tempos
Changes in meter are frequent, but they don't seem to conform to a plan and seem to serve only to aid performance. In any case, a rhythmic sensation is generally absent in these pages. Sometimes it arises for a few seconds, but is immediately cancelled out.

This is how the first page of the score that you can listen to here:

Back